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shreya n Grade: 12
        

integrate frm -1 to 1:
 [x+[x+[x]]]dx



6 years ago

Answers : (2)

Davis Devasia
31 Points
										

Don't you know that you can cut this integration to two parts?


ie, -11 f(x).dx = -10 f(x).dx + 01 f(x).dx


Let f(x) = [x]


By the defenition of [x]; we have,


f(x) = x, x>0 and f(x) = -x, x<0


Then, come to your problem,


Let g(x) = [x+[x+[x]]].


When x>0; g(x) = x+x+x = 3x;


When x<0; g(x) = -x; (Why?? Do it yourself!!)


Then your problem reduces to:


-11 [x+[x+[x]]].dx


= -10 (-x).dx + 01 3x.dx


= -(0/2) - (-1/2) + (3*1/2) - 0


= +(1/2) + (3/2)


= 2.


Is this the correct answer??

6 years ago
Davis Devasia
31 Points
										

Sorry Sorry! I misunderstood your question! I'm extremely sorry!


I thought that [x] is modulus function! I thought of "greatest integer function" just after clicking "POST REPLY" button!


I couldn't undo it!


Again, extremely sorry for wasting your time!!

6 years ago
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